Mathematics and the Physical Universe

July 4, 2008

By Dr. David Rogstad

More than once, scientists and philosophers have noted how mathematics can describe, with remarkable precision, the laws that govern our universe. An example of this is found in the articleThe Unreasonable Effectiveness of Mathematics in the Natural Sciences by the Nobel Prize-winning physicist, Eugene Wigner. (See also a discussion here.) Mathematics is largely a product of human minds, using reason and logic, while the laws of physics are a description of how the cosmos operates. Why should there be any relationship between the two? Why, for instance, should the motion of Earth around the Sun follow a pattern that derives precisely from an inverse square law, a purely algebraic expression? As a naturalist with some Hindu leanings, Wigner commented:

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

A further example of the correspondence between mathematics and physics has been published in the Notices of the American Mathematical Society by D. Khavinson and G. Neumann, and described in less technical terms in a press release here. These authors were working on an extension of a fundamental theorem in their particular field of mathematics. Without going into the details of their work, Khavinson and Neumann were able to derive an upper bound for the number of solutions to a certain type of equation. They posted their result on the Web, expecting no one outside the field of mathematics would be interested.

To their great surprise, they received a response from an astrophysicist S. Rhie, who had been studying gravitational lensing, where light from a distant celestial object, such as a star or galaxy, is deflected by a massive object between the source of light and the observer. This phenomenon was originally predicted using Newtonian mechanics, and refined using Einstein’s general relativity. The first gravitational lensing was discovered in 1979. Rhie was working on certain idealized situations where the number of images that could be seen due to gravitational lensing could be calculated mathematically. He used the same forms investigated by Khavinson and Neumann and obtained the same result, with some additional improvements.

While such a connection between mathematics and physics is hardly new, it supplies one more reminder of this amazing relationship. The atheist says matter created mind, providing no explanation for this correspondence. The theist says mind created matter, in which case the correspondence makes perfect sense. Humans are capable of thinking some of God’s thoughts after Him, the one who used His mind to create the wonderful cosmos in which we live.

Subjects:
Laws of Physics, Logic, Naturalism

Dr. David Rogstad

Dr. Dave Rogstad received his PhD in physics from Caltech and worked over 30 years for NASA’s Jet Propulsion Laboratory. Though now retired, Dave continues to serve as an RTB board member and participates regularly in several RTB podcasts.

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